This will be my first year of hunting some large bodied northern whitetails and I am not sure which
ammo would be best for this task. I have not yet shot any animal with this rifle so not sure what
round to shoot. I don't plan on shooting anything else other than hogs and coyotes and maybe a stray
Nilgai that roams across our ranch in south Texas. Any suggestions would be greatly appreciated.

I wouldn't take it. Sure, it's plenty of gun but those big bodied northern deer are tough and are often steps away from deep ravines (if you're hunting in the Midwest). I love to shoot my .257 WBY and have killed deer weighing between 230-240 lbs on the hoof with it.

I shoot 99% of my whitetails with a 7mm-08 and soft nosed bullet. But when I'm hunting big, heavy bodied trophy deer, I shoot a 300 RUM with a 180 grain Swift Scirocco bullet. Square through both shoulders and they never take a step. And that would be the PERFECT round for Nilgai.

If you insist on the .257, I'd shoot either a 120 gr. Nosler Partition, a 115 gr. Berger VLD or a 115 Barnes Triple Shock.

Only other rifles I have are a 6mm, .243 and .22-250 and a .50 cal muzzle loader.
What off the shelf Weatherby .257 should I buy?

Shoot any of the three bullets I mentioned and you should be fine.

Haven't seen anything argue with a 257 Wby shooting 120gr partitions or 110gr accubonds. From whitetails to elk thise seem to work fine

Thank you gentlemen, gotta go get some ammo.

Accubonds, Partitions, Scirroccos, A-Frame should all be good to go. Never cared for mono metal like the TSX, TTSX. VLD reports I am hearing are all over the place. Some love them, some hate them.

For the bigger Nilgai, I'd suggest the 120 Nosler Partition for penetration. Second choice would be 110g Nosler Accubond. I have no personal experience with the other rounds mentioned above.